Elucidating the Mechanical Properties of Crystalline Interfaces from Thermal Fluctuations

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Nanostructured materials have gained prominence owing to the exciting array of physical properties that are primarily governed by the high density of interfaces and interfacial phenomena. This dissertation presents the statistical mechanics modeling and atomistic simulations of two types of crystalline interfaces, namely twin boundaries and grain boundaries, to understand their thermodynamic and kinetic properties based on thermal fluctuations.

To this end, we first study the thermal fluctuations of twin boundaries in face-centered-cubic metals to elucidate the deformation mechanism governing their kinetic properties. Our simulations show that the normal motion of twin boundaries is strongly coupled to shear deformation up to near the melting temperature. Since twin boundaries commonly occur as parallel interfaces, we further investigate the entropic interaction between fluctuating twin boundaries using atomistic simulations and statistical mechanics based analysis. The simulations reveal that fluctuations of twin boundaries are enhanced in the presence of adjoining twin boundaries as their spacing d decreases. In addition, the theoretical analysis shows that fluctuating twin boundaries indeed exhibit an attractive entropic interaction which enhances their thermal fluctuations and that this force decreases as 1/d^2. This attractive interaction between twin boundaries is attributed to their shear coupled normal motion and is fundamentally distinct from the well -known repulsive entropic interaction followed by fluid membranes and many crystalline membranes and interfaces.

In addition to the entropic force, we present a study of the thermal expansion of twin boundaries at finite temperature by way of atomistic simulations. The simulations reveal that for all twin boundary spacing d, the thermal expansion induced stress varies as 1/d. This long-range effect is attributed to the inhomogeneity in the thermal expansion coefficient due to the interfacial regions.

Finally, we study the effect of defects, specifically second phase particles, in grain boundaries by extending the interface random walk model, and deriving the general analytical expression relating the grain boundary mobility to key parameters governing the interaction between the particles and the grain boundary. We verify our theoretical model through atomistic simulations for symmetrical tilt boundaries with multiple fixed inclusions and propose a method to extract the mobility from grain boundary fluctuations.

Crystalline Interfaces, Grain boundaries, Twin boundaries, Molecular dynamics, Thermal fluctuations, Entropic Interaction
Portions of this document appear in: Chen, Dengke, and Yashashree Kulkarni. "Elucidating the kinetics of twin boundaries from thermal fluctuations." MRS Communications 3, no. 4 (2013): 241-244. And in: Chen, Dengke, and Yashashree Kulkarni. "Entropic interaction between fluctuating twin boundaries." Journal of the Mechanics and Physics of Solids 84 (2015): 59-71. And in: Chen, Dengke, and Yashashree Kulkarni. "Atomistic study of the thermal stress due to twin boundaries." Journal of Applied Mechanics 82, no. 2 (2015): 021005.